A System of Popular Geometry: Containing in a Few Lessons So Much of the Elements of Euclid as is Necessary and Sufficient for a Right Understanding of Every Art and Science in Its Leading Truths and General PrinciplesTaylor and Walton, Booksellers to the University of London, 30 Upper Gower Street, 1836 - 128 sider |
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Side vi
... demonstrating its adequacy as well as simplicity . We did not give this explanation in our First Edition from an unwillingness to perplex a beginner , and lengthen our book with what then appeared needless . We thought that our readers ...
... demonstrating its adequacy as well as simplicity . We did not give this explanation in our First Edition from an unwillingness to perplex a beginner , and lengthen our book with what then appeared needless . We thought that our readers ...
Side vii
... demonstration of ART . 20 , & c . Of the sup- pressed element , which is the objectionable one in Euclid , those who desire it may see , in the section of Useful Re- sults , a complete demonstration from our principles , that given in ...
... demonstration of ART . 20 , & c . Of the sup- pressed element , which is the objectionable one in Euclid , those who desire it may see , in the section of Useful Re- sults , a complete demonstration from our principles , that given in ...
Side xii
... demonstrations of propositions as plain for the mind , and as brief for the memory , as possible . For this purpose we have made several alterations : Instead of notes of reference , which distract the mind , we have introduced the ...
... demonstrations of propositions as plain for the mind , and as brief for the memory , as possible . For this purpose we have made several alterations : Instead of notes of reference , which distract the mind , we have introduced the ...
Side xiii
... demonstrations on a false premise . By doing a Problem actually , we prove that it can be done ; nor is there any other method of being sure that we may suppose it in a demonstration . But as there are no pro- * Such as PROP . 7th ...
... demonstrations on a false premise . By doing a Problem actually , we prove that it can be done ; nor is there any other method of being sure that we may suppose it in a demonstration . But as there are no pro- * Such as PROP . 7th ...
Side xiv
... demonstrations , according as they are wanted ; instead of loading the memory and revolting the taste with a number of barren truisms , before their utility is perceivable . Besides , the latter , formed as they are by rather a painful ...
... demonstrations , according as they are wanted ; instead of loading the memory and revolting the taste with a number of barren truisms , before their utility is perceivable . Besides , the latter , formed as they are by rather a painful ...
Vanlige uttrykk og setninger
ABCD altitudes angle ABC angle BAC angle CDA angles EAB angles equal base AC centre chord circumference Consequently contained definition demonstration equal arches equal bases equal circles equal sides equal to CD equal to four equal triangles equally distant equi-angular Euclid finite right line Geometry given finite right given point given right line greater Hence ibid internal angles Join KLMN Let ABC line CD lines be drawn magnitude NOTE opposite angles parallel right lines parallelogram perpendicular PROB produced propositions quantities reciprocally proportional rectangle rectilineal figure respectively equal right angles right line divided right line drawn right line intersect segments side AB side AC square of AB square of AC submultiple supposition is false tangent theorem third side three sides tiples triangle ABC unequal vertex
Populære avsnitt
Side 31 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.
Side xxxi - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 3 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Side xxx - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 30 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.
Side 25 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.
Side 99 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Side 51 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...
Side 10 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 11 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.